Not all Tuition Exchange schools offer full tuition to all eligible students. You can use http://www.tuitionexchange.org/vnews/display.v/SEC/Families|School%20Search to check for percentages of eligible students getting the awards, the size of the awards, and other factors relating to the awards.
For your safeties, you may want to choose schools where all eligible students get the awards, if the award is necessary for the school to be within your budget (considering that money saved or debt avoided in undergraduate can help if you go to expensive medical school).